## Linear Operators: Spectral theory |

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Page 909

Spectral Representation Let u be a finite positive measure defined on the

Spectral Representation Let u be a finite positive measure defined on the

**Borel**sets B of the complex plane and vanishing on the complement of a bounded set S. One of the simplest examples of a bounded normal operator is the operator T ...Page 913

Let E be the spectral resolution for T and let vn ( e ) = ( E ( e ) yn , yn ) for each

Let E be the spectral resolution for T and let vn ( e ) = ( E ( e ) yn , yn ) for each

**Borel**set e . Using the Lebesgue decomposition theorem ( III.4.14 ) , let { en } be a sequence of**Borel**sets such that Li ...Page 1900

( See also Boolean ring ) definition , ( 43 ) properties , ( 44 ) representation of , ( 44 ) Boolean ring , definition , ( 40 ) representation of , 1.12.1 ( 41 )

( See also Boolean ring ) definition , ( 43 ) properties , ( 44 ) representation of , ( 44 ) Boolean ring , definition , ( 40 ) representation of , 1.12.1 ( 41 )

**Borel**field of sets , definition , III.5.10 ( 137 )**Borel**function , X.1 ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Miscellaneous Applications | 937 |

Compact Groups | 945 |

Copyright | |

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